User:Benjah-bmm27/degree/3/MFH

Crystallography, MFH

Texts

• Otterbein College: learn molecular symmetry with Jmol
• Werner Massa, Crystal Structure Determination (2004)
• Bill (William) Clegg, Crystal Structure Determination (Oxford Chemistry Primer) (1998)
• Glusker, J. P.; Lewis, M.; Rossi, M. Crystal Structure Analysis for Chemists and Biologists.
• International Tables for Crystallography Volume C. doi:10.1107/97809553602060000103.
  • Book review: Acta Cryst. (2007). A63, 483

Topics

• Crystallography
• Structural analysis

Unit cells, lattices and symmetry

• Molecular structure and crystal structure
• Crystal shapes, including symmetry axes
  • Calcite — cubic
  • Molybdenite — hexagonal
  • Diamond — cubic

Crystal symmetry

• Symmetry
  • Point symmetry
  • Translational symmetry
  • Symmetry groups
    • In one dimension: 7 frieze groups
    • In two dimensions: 17 wallpaper groups
    • In three dimensions: 230 space groups (list)
• Crystallographic restriction theorem — cannot have 5-fold rotation symmetry in crystal lattices (pentagons don't tessellate)
• Symmetry elements in crystallography
  • Hermann–Mauguin notation
  • Screw axes
  • Glide planes

Crystal systems

• 7 crystal systems

crystal system	cell edge restriction	cell angle restriction
triclinic	none	none
monoclinic	none	α = γ = 90°
orthorhombic	none	α = β = γ = 90°
tetragonal	a = b	α = β = γ = 90°
trigonal, hexagonal	a = b	α = β = 90°, γ = 120°
cubic	a = b = c	α = β = γ = 90°

Bravais lattices

• 14 Bravais lattices

pearson symbol	lattice name	commonly called
aP	triclinic	?
mP	monoclinic primitive	?
mC	monoclinic C-centred	?
oP	orthorhombic primitive	?
oA	orthorhombic A-centred	?
oI	orthorhombic body centred	?
oF	orthorhombic (all-)face centred	?
tP	tetragonal primitive	?
tI	tetragonal body centred	?
hP	trigonal or hexagonal primitive	?
hR	rhombohedral, hexagonal setting	?
cP	cubic primitive	simple cubic
cI	cubic body-centred	body-centred cubic
cF	cubic (all-)face centred	face-centred cubic

Miller indices

• Lattice planes
• Miller indices (hkl) and all that - http://www.doitpoms.ac.uk/tlplib/miller_indices/index.php

Bragg's law

• Bragg's law
• Bragg diffraction

Misc

• Structure factor
• Patterson function
• X-ray notation
• Fractional coordinates

Systematic absences

absence	when this is odd	indicates presence of this symmetry element
h00	h	21 screw axis parallel to the a-axis
0k0	k	21 screw axis parallel to the b-axis
00l	l	21 screw axis parallel to the c-axis
h0l	h	a-glide perpendicular to the b-axis
h0l	l	c-glide perpendicular to the b-axis
h0l	h+l	n-glide perpendicular to the b-axis
hkl	k+l	A-centred
hkl	h+l	B-centred
hkl	h+k	C-centred
hkl	h+k+l	I-centred
hkl	one or two but not all three of h, k, and l	F-centred

Solving the Phase Problem, Refinement of the Solution and Interpretation of the Results

• Direct methods
• Structure refinement
• R-factors
• Measurement errors
• Weighting
• Accuracy of results

A cautionary tale: the quest for cyclopentadienyl cation

• Cyclopentadienyl cation, [C₅H₅]⁺
• Pentamethylcyclopentadienyl cation, [C₅Me₅]⁺, AKA [Cp*]⁺, should be stable, thought they'd determined a crystal structure containing it
• Turned out to be the pentamethylcyclopentenyl cation, [(CMe)₃(CHMe)₂]⁺
• http://www.benjamin-mills.com/chemistry/structures/Cp*-cation/

C10H15+ pentamethylcyclopentadienyl cation	C10H17+ pentamethylcyclopentenyl cation

See also

• User:Benjah-bmm27/degree#Crystallography
• Symmetry in Crystallography from the University of Oklahoma Chemical Crystallography Lab
• X-ray Diffraction Techniques, an interactive tutorial from the University of Cambridge